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Simplifying (5p + 1)(p + 4) = 2(7p + 5) Reorder the terms: (1 + 5p)(p + 4) = 2(7p + 5) Reorder the terms: (1 + 5p)(4 + p) = 2(7p + 5) Multiply (1 + 5p) * (4 + p) (1(4 + p) + 5p * (4 + p)) = 2(7p + 5) ((4 * 1 + p * 1) + 5p * (4 + p)) = 2(7p + 5) ((4 + 1p) + 5p * (4 + p)) = 2(7p + 5) (4 + 1p + (4 * 5p + p * 5p)) = 2(7p + 5) (4 + 1p + (20p + 5p2)) = 2(7p + 5) Combine like terms: 1p + 20p = 21p (4 + 21p + 5p2) = 2(7p + 5) Reorder the terms: 4 + 21p + 5p2 = 2(5 + 7p) 4 + 21p + 5p2 = (5 * 2 + 7p * 2) 4 + 21p + 5p2 = (10 + 14p) Solving 4 + 21p + 5p2 = 10 + 14p Solving for variable 'p'. Reorder the terms: 4 + -10 + 21p + -14p + 5p2 = 10 + 14p + -10 + -14p Combine like terms: 4 + -10 = -6 -6 + 21p + -14p + 5p2 = 10 + 14p + -10 + -14p Combine like terms: 21p + -14p = 7p -6 + 7p + 5p2 = 10 + 14p + -10 + -14p Reorder the terms: -6 + 7p + 5p2 = 10 + -10 + 14p + -14p Combine like terms: 10 + -10 = 0 -6 + 7p + 5p2 = 0 + 14p + -14p -6 + 7p + 5p2 = 14p + -14p Combine like terms: 14p + -14p = 0 -6 + 7p + 5p2 = 0 Factor a trinomial. (-2 + -1p)(3 + -5p) = 0Subproblem 1
Set the factor '(-2 + -1p)' equal to zero and attempt to solve: Simplifying -2 + -1p = 0 Solving -2 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1p = 0 + 2 -1p = 0 + 2 Combine like terms: 0 + 2 = 2 -1p = 2 Divide each side by '-1'. p = -2 Simplifying p = -2Subproblem 2
Set the factor '(3 + -5p)' equal to zero and attempt to solve: Simplifying 3 + -5p = 0 Solving 3 + -5p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5p = 0 + -3 -5p = 0 + -3 Combine like terms: 0 + -3 = -3 -5p = -3 Divide each side by '-5'. p = 0.6 Simplifying p = 0.6Solution
p = {-2, 0.6}
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